A new method of calculating crown projection area and its comparative accuracy with conventional calculations for asymmetric tree crowns

This paper introduces a new method of calculating crown projection area (CPA), the area of level ground covered by a vertical projection of a tree crown from measured crown radii through numerical interpolation and integration. This novel method and other four existing methods of calculating CPA were compared using detailed crown radius measurements from 30 tall trees of Eucalyptus pilularis variable in crown size, shape, and asymmetry. The four existing methods included the polygonal approach and three ways of calculating CPA as the area of a circle using the arithmetic, geometric and quadratic mean radius. Comparisons were made across a sequence of eight non-consecutive numbers (from 2 to 16) of measured crown radii for each tree over the range of crown asymmetry of the 30 trees through generalized linear models and multiple comparisons of means. The sequence covered the range of the number of crown radii measured for calculating the CPA of a tree in the literature. A crown asymmetry index within the unit interval was calculated for each tree to serve as a normative measure. With a slight overestimation of 2.2